You are right that in normal times all the money that got saved would be snapped up by businesses that wanted to expand. However, our current situation can give you some idea as to why Keynes did not believe this would always happen.

Right after the late 2008 crash (and even to some extent now) banks were not really willing to lend. They did not believe they would get their money back. Similarly, at times...

You are right that in normal times all the money that got saved would be snapped up by businesses that wanted to expand. However, our current situation can give you some idea as to why Keynes did not believe this would always happen.

Right after the late 2008 crash (and even to some extent now) banks were not really willing to lend. They did not believe they would get their money back. Similarly, at times businesses are not willing to invest because they do not think there will be enough demand to make it worth it for them to invest in new machinery, for example.

So Keynes thought that demand had to come first. He did not believe that more money available to borrow would actually lead to more borrowing.